<!DOCTYPE html>
<html lang="en-US">
<!--********************************************-->
<!--*       Generated from PreTeXt source      *-->
<!--*                                          *-->
<!--*         https://pretextbook.org          *-->
<!--*                                          *-->
<!--********************************************-->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="robots" content="noindex, nofollow">
</head>
<body class="ignore-math">
<h3 class="heading"><span class="type">Paragraph</span></h3>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
W_1=\left| 
\begin{array}{ccc}
0&amp; e^x &amp; e^{-x}\\
0 &amp; e^x &amp; -e^{-x}\\
1 &amp; e^x &amp; e^{-x}
\end{array}
\right|=-2,\quad W_2=\left| 
\begin{array}{ccc}
1&amp; 0 &amp; e^{-x}\\
0 &amp;0 &amp; -e^{-x}\\
0 &amp;1 &amp; e^{-x}
\end{array}
\right|=e^{-x},\quad W_3=\left| 
\begin{array}{ccc}
1&amp; e^x &amp; 0\\
0 &amp; e^x &amp;0\\
0 &amp; e^x &amp;1
\end{array}
\right|=e^x.
\end{equation*}
</div>
<span class="incontext"><a href="sec4_4.html#p-172" class="internal">in-context</a></span>
</body>
</html>
